Co-channel interference rejection for MIMO-OFDM systems

A method based on the maximum a posteriori probability （MAP） criterion is proposed to estimate the channel frequency response （CFR） matrix and interference- plus-noise spatial covariance matrix （SCM） for multiple input and multiple output orthogonal frequency division multiplexing （MIMO-OFDM） systems. An iterative solution is proposed to solve the MAP-based problem and an interference rejection combining （IRC） receiver is derived to suppress co-channel interference （CCI） based on the estimated CFR and SCM. Furthermore, considering the property of SCM, i. e., Hermitian and semi-definite, two schemes are proposed to improve the accuracy of SCM estimation. The first scheme is proposed to parameterize the SCM via a sum of a series of matrices in the time domain. The second scheme measures the SCM on each subcarrier as a low-rank model while the model order can be chosen through the penalized-likelihood approach. Simulation results are provided to demonstrate the effectiveness of the proposed method.

High dimensional covariance matrix estimation using multi-factor models from incomplete information

Covariance matrix plays an important role in risk management, asset pricing, and portfolio allocation. Covariance matrix estimation becomes challenging when the dimensionality is comparable or much larger than the sample size. A widely used approach for reducing dimensionality is based on multi-factor models. Although it has been well studied and quite successful in many applications, the quality of the estimated covariance matrix is often degraded due to a nontrivial amount of missing data in the factor matrix for both technical and cost reasons. Since the factor matrix is only approximately low rank or even has full rank, existing matrix completion algorithms are not applicable. We consider a new matrix completion paradigm using the factor models directly and apply the alternating direction method of multipliers for the recovery. Numerical experiments show that the nuclear-norm matrix completion approaches are not suitable but our proposed models and algorithms are promising.

High Dimensionality Effects on the Efficient Frontier: A Tri-Nation Study

Markowitz Portfolio theory under-estimates the risk associated with the return of a portfolio in case of high dimensional data. El Karoui mathematically proved this in [1] and suggested improved estimators for unbiased estimation of this risk under specific model assumptions. Norm constrained portfolios have recently been studied to keep the effective dimension low. In this paper we consider three sets of high dimensional data, the stock market prices for three countries, namely US, UK and India. We compare the Markowitz efficient frontier to those obtained by unbiasedness corrections and imposing norm-constraints in these real data scenarios. We also study the out-of-sample performance of the different procedures. We find that the 2-norm constrained portfolio has best overall performance.